{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adversarial Variational Bayes\n",
    "This notebook contains the code for the STAN example to demonstrate how Adversarial Variational Bayes (AVB) can be used to approximate complex posterior distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import os\n",
    "import pystan\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import ite\n",
    "from tqdm import tqdm_notebook\n",
    "import re\n",
    "import glob\n",
    "import tensorflow as tf\n",
    "from tensorflow.contrib import slim\n",
    "ds = tf.contrib.distributions\n",
    "st = tf.contrib.bayesflow.stochastic_tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parameters\n",
    "batch_size = 512\n",
    "data = {'J': 8,\n",
    "        'y': [2.8,  0.8, -0.3,  0.7, -0.1,  0.1, 1.8, 1.2],\n",
    "       'sigma': [0.8, 0.5, 0.8, 0.6,  0.5, .6, 0.5, 0.4],\n",
    "       'psigma_eta': 1., 'psigma_mu': 1., 'psigma_tau': 1.}\n",
    "\n",
    "# Parameter for AVB: wether to use adaptive contrast\n",
    "is_adapt_contrast = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Utility functions\n",
    "def kde(mu, tau, bbox=[-5, 5, -5, 5], xlabel=\"\", ylabel=\"\"):\n",
    "    values = np.vstack([mu, tau])\n",
    "    kernel = sp.stats.gaussian_kde(values)\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.axis(bbox)\n",
    "    ax.set_aspect(4/5*abs(bbox[1]-bbox[0])/abs(bbox[3]-bbox[2]))\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "\n",
    "    xx, yy = np.mgrid[bbox[0]:bbox[1]:100j, bbox[2]:bbox[3]:100j]\n",
    "    positions = np.vstack([xx.ravel(), yy.ravel()])\n",
    "    f = np.reshape(kernel(positions).T, xx.shape)\n",
    "    cfset = ax.contourf(xx, yy, f, cmap='Blues')\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "def scatter(mu, tau, bbox=[-5, 5, -5, 5], xlabel=\"\", ylabel=\"\"):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.axis(bbox)\n",
    "    ax.set_aspect(4/5*abs(bbox[1]-bbox[0])/abs(bbox[3]-bbox[2]))\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "                        \n",
    "    ax.scatter(mu, tau, edgecolor='none', alpha=0.5)\n",
    "\n",
    "    plt.show()    \n",
    "\n",
    "    \n",
    "def hist(x, xlabel=\"\", ylabel=\"\"):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.hist(x, bins=50)\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "def heat_map(f, bbox=[-5, 5, -5, 5], xlabel=\"\", ylabel=\"\"):\n",
    "    if not os.path.exists(output_dir):\n",
    "        os.makedirs(output_dir)\n",
    "    N, M = f.shape\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.axis(bbox)\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "                        \n",
    "    xx, yy = np.mgrid[bbox[0]:bbox[1]:(N*1j), bbox[2]:bbox[3]:(M*1j)]\n",
    "    cfset = ax.contourf(xx, yy, f, cmap='Reds')\n",
    "    cset = ax.contour(xx, yy, f, colors='k')\n",
    "    plt.show()\n",
    "\n",
    "def heat_map_func(func, data, bbox=[-5, 5, -5, 5], **kwargs):\n",
    "    xx, yy = np.mgrid[bbox[0]:bbox[1]:100j, bbox[2]:bbox[3]:100j]\n",
    "    positions = np.vstack([xx.ravel(), yy.ravel()])\n",
    "    f = np.reshape(func(positions, data=data).T, xx.shape)\n",
    "    heat_map(f, bbox, **kwargs)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Models\n",
    "Select one of the following models by running the associated code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eight schools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_00dad1eb4bc86a34204f8b1210adf4a7 NOW.\n"
     ]
    }
   ],
   "source": [
    "model_code = \"\"\"\n",
    "data {\n",
    "  int<lower=0> J; // number of schools \n",
    "  real y[J]; // estimated treatment effects\n",
    "  real<lower=0> sigma[J]; // s.e. of effect estimates \n",
    "  real<lower=0> psigma_eta; // prior for eta\n",
    "  real<lower=0> psigma_mu; // prior for mu\n",
    "  real<lower=0> psigma_tau; // prior for tau\n",
    "\n",
    "}\n",
    "parameters {\n",
    "  real mu; \n",
    "  real tau;\n",
    "  real eta[J];\n",
    "}\n",
    "transformed parameters {\n",
    "  real theta[J];\n",
    "  for (j in 1:J)\n",
    "    theta[j] = mu + tau * eta[j];\n",
    "}\n",
    "model {\n",
    "  target += normal_lpdf(y | theta, sigma);\n",
    "  target += normal_lpdf(eta | 0, psigma_eta);\n",
    "  target += normal_lpdf(mu | 0, psigma_mu);\n",
    "  target += normal_lpdf(tau | 0, psigma_tau);\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "sm = pystan.StanModel(model_code=model_code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "param_dim = 2 + data['J']\n",
    "Ez0 = np.zeros(param_dim, dtype=np.float32)\n",
    "stdz0 = np.concatenate([\n",
    "            np.array([data['psigma_mu'], data['psigma_tau']], dtype=np.float32),\n",
    "            data[\"psigma_eta\"] * np.ones(data['J'], dtype=np.float32)\n",
    "        ])\n",
    "def get_logprob(z, data):\n",
    "    mu = z[:, 0:1]\n",
    "    tau = z[:, 1:2]\n",
    "    eta = z[:, 2:]\n",
    "    theta = mu + tau*eta\n",
    "\n",
    "    y = tf.constant(data['y'], dtype=tf.float32, shape=(1, data['J']))\n",
    "    sigma = tf.constant(data['sigma'], dtype=tf.float32, shape=(1, data['J']))\n",
    "    err = (y - theta)/sigma\n",
    "\n",
    "    logprob = tf.reduce_sum(\n",
    "        -0.5 * tf.square(err) - tf.log(sigma) - 0.5*np.log(2*np.pi), [1]\n",
    "    )\n",
    "    logprob -= 0.5*tf.reduce_sum(tf.square(mu/data['psigma_mu']), [1])\n",
    "    logprob -= 0.5*tf.reduce_sum(tf.square(tau/data['psigma_tau']), [1])\n",
    "    logprob -= 0.5*tf.reduce_sum(tf.square(eta/data['psigma_eta']), [1])\n",
    "    \n",
    "    return logprob\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gauss example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_code = \"\"\"\n",
    "data {\n",
    "  int<lower=0> J; // number of schools \n",
    "  real y[J]; // estimated treatment effects\n",
    "}\n",
    "parameters {\n",
    "  real mu;\n",
    "  real logsigma;\n",
    "}\n",
    "model {\n",
    "  target += normal_lpdf(mu | 0, 100);\n",
    "  target += normal_lpdf(logsigma | 0, 100);\n",
    "  target += normal_lpdf(y | mu, exp(logsigma));\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "sm = pystan.StanModel(model_code=model_code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_dim = 2\n",
    "Ez0 = np.array([0., 0.], dtype=np.float32)\n",
    "stdz0 = np.array([100., 100.], dtype=np.float32)\n",
    "\n",
    "def get_logprob(z, data):\n",
    "    mu = z[:, 0:1]\n",
    "    logsigma = z[:, 1:2]\n",
    "    y = np.asarray(data['y'], dtype=np.float32).reshape(1, -1)\n",
    "    err = (y - mu)*tf.exp(-logsigma)\n",
    "\n",
    "    logprob = tf.reduce_sum(\n",
    "        -0.5 * tf.square(err) - logsigma - 0.5*np.log(2*np.pi), [1]\n",
    "    )\n",
    "    logprob -= 0.5*tf.reduce_sum(z/stdz0.reshape(1, -1), [1])\n",
    "    return logprob\n",
    "\n",
    "\n",
    "def get_logprob_np(z, data):\n",
    "    mu = z[:, 0:1]\n",
    "    logsigma = z[:, 1:2]\n",
    "    y = np.asarray(data['y'], dtype=np.float32).reshape(1, -1)\n",
    "    err = (y - mu)*np.exp(-logsigma)\n",
    "\n",
    "    logprob = np.sum( \n",
    "        -0.5 * err*err - logsigma - 0.5*np.log(2*np.pi), axis=1\n",
    "    )\n",
    "    logprob -= 0.5*np.sum(z/stdz0.reshape(1, -1), axis=1)\n",
    "    return logprob\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rosenbrock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_dim = 2\n",
    "Ez0 = np.array([0., 0.], dtype=np.float32)\n",
    "stdz0 = np.array([1000., 1000.], dtype=np.float32)\n",
    "\n",
    "def get_logprob(z, data):\n",
    "    x1 = z[:, 0:1]\n",
    "    x2 = z[:, 1:2]\n",
    "        \n",
    "    logprob = tf.reduce_sum(\n",
    "        -tf.square(x1 - 1) - tf.square(tf.square(x2) - x1), [1]\n",
    "    )\n",
    "    return logprob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Torus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "param_dim = 2\n",
    "Ez0 = np.array([0., 0.], dtype=np.float32)\n",
    "stdz0 = np.array([1000., 1000.], dtype=np.float32)\n",
    "\n",
    "def get_logprob(z, data):\n",
    "    x1 = z[:, 0:1]\n",
    "    x2 = z[:, 1:2]\n",
    "        \n",
    "    logprob = tf.reduce_sum(\n",
    "        -tf.square((tf.square(x1) + tf.square(x2)) - 2.), [1]\n",
    "    )\n",
    "\n",
    "    return logprob\n",
    "\n",
    "def torus_np(z):\n",
    "    x1 = z[:, 0:1]\n",
    "    x2 = z[:, 1:2]\n",
    "        \n",
    "    logprob = np.sum(\n",
    "        -np.square(x1*x1 + x2*x2 - 2.), axis=1\n",
    "    )\n",
    "\n",
    "    return logprob\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AVB definition\n",
    "The main code for AVB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lrelu(x, leak=0.2, name=\"lrelu\"):\n",
    "    return tf.maximum(x, leak*x)\n",
    "\n",
    "def standard_normal(shape, **kwargs):\n",
    "    \"\"\"Create a standard Normal StochasticTensor.\"\"\"\n",
    "    return st.StochasticTensor(\n",
    "        ds.MultivariateNormalDiag(mu=tf.zeros(shape), diag_stdev=tf.ones(shape), **kwargs))\n",
    "\n",
    "def posterior(reuse=False):\n",
    "    with tf.variable_scope(\"posterior\", reuse=reuse) as scope:\n",
    "        eps = standard_normal([batch_size, param_dim]).value()\n",
    "\n",
    "        with slim.arg_scope([slim.fully_connected], activation_fn=tf.nn.elu):\n",
    "            net = slim.fully_connected(eps, 128, scope='fc_0')\n",
    "            net = slim.fully_connected(net, 128, scope='fc_1')\n",
    "#             net = slim.fully_connected(net, 128, scope='fc_2')\n",
    "                \n",
    "        z = slim.fully_connected(net, param_dim, activation_fn=None, scope='z')\n",
    "\n",
    "        return z\n",
    "\n",
    "def adversary(z, reuse=False):\n",
    "    with tf.variable_scope(\"adversary\", reuse=reuse) as scope:\n",
    "        with slim.arg_scope([slim.fully_connected], activation_fn=lrelu):\n",
    "            net = slim.fully_connected(z, 256, scope='fc_0')\n",
    "\n",
    "            for i in range(5):\n",
    "                dnet = slim.fully_connected(net, 256, scope='fc_%d_r0' % (i+1))\n",
    "                net += slim.fully_connected(dnet, 256, activation_fn=None, scope='fc_%d_r1' % (i+1),\n",
    "                                            weights_initializer=tf.constant_initializer(0.))\n",
    "                net = lrelu(net) \n",
    "\n",
    "        T = slim.fully_connected(net, 1, activation_fn=None, scope='T',\n",
    "                                weights_initializer=tf.constant_initializer(0.))\n",
    "        T = tf.squeeze(T, [1])\n",
    "        return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "tf.reset_default_graph() \n",
    "z0 = tf.random_normal([batch_size, param_dim], name=\"z0\")\n",
    "z_ = posterior()\n",
    "beta = tf.constant(1.)\n",
    "\n",
    "if is_adapt_contrast:\n",
    "    Ez_, Varz_ = tf.nn.moments(z_, [0], keep_dims=True)\n",
    "    stdz_ = tf.sqrt(Varz_) + 1e-6\n",
    "    Ez_ = tf.stop_gradient(Ez_)\n",
    "    stdz_ = tf.stop_gradient(stdz_)\n",
    "else:\n",
    "    Ez_ = tf.constant(Ez0.reshape(1, -1), dtype=tf.float32)\n",
    "    stdz_ = tf.constant(stdz0.reshape(1, -1), dtype=tf.float32)\n",
    "\n",
    "zr = Ez_ + stdz_ * z0\n",
    "znorm_ = (z_ - Ez_) / stdz_\n",
    "\n",
    "logr_ = -tf.reduce_sum(0.5 * tf.square(znorm_) + tf.log(stdz_) + 0.5 * np.log(2*np.pi), [1])\n",
    "logr_zr = -tf.reduce_sum(0.5 * tf.square(z0) + tf.log(stdz_) + 0.5 * np.log(2*np.pi), [1])\n",
    "    \n",
    "if is_adapt_contrast:\n",
    "    Ti = adversary(z0) - logr_zr\n",
    "    Td = adversary(znorm_, reuse=True) - logr_\n",
    "else:\n",
    "    Ti = adversary(zr) - logr_zr\n",
    "    Td = adversary(z_, reuse=True) - logr_\n",
    "\n",
    "\n",
    "logprob = get_logprob(z_, data)\n",
    "mean_logprob = tf.reduce_mean(logprob)\n",
    "mean_Td = tf.reduce_mean(Td)\n",
    "loss_primal = tf.reduce_mean(beta*(logr_ + Td) - logprob)\n",
    "\n",
    "d_loss_d = tf.reduce_mean(\n",
    "   tf.nn.sigmoid_cross_entropy_with_logits(logits=Td, labels=tf.ones_like(Td))\n",
    ")\n",
    "d_loss_i = tf.reduce_mean(\n",
    "    tf.nn.sigmoid_cross_entropy_with_logits(logits=Ti, labels=tf.zeros_like(Ti))\n",
    ")\n",
    "loss_dual = d_loss_i + d_loss_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pvars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, \"posterior\")\n",
    "dvars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, \"adversary\")\n",
    "popt = tf.train.AdamOptimizer(1e-4, beta1=0.5)\n",
    "dopt = tf.train.AdamOptimizer(2e-4, beta1=0.5)\n",
    "\n",
    "grads_primal =  popt.compute_gradients(loss_primal, var_list=pvars)\n",
    "grads_dual = dopt.compute_gradients(loss_dual, var_list=dvars)\n",
    "\n",
    "train_primal = popt.apply_gradients(grads_primal)\n",
    "train_dual = dopt.apply_gradients(grads_dual)\n",
    "\n",
    "train_step = [train_primal, train_dual]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from tqdm import tqdm_notebook, tnrange\n",
    "\n",
    "def run_training(sess, data, niter=10000, betas=None, npretrain=0):       \n",
    "    if betas is None:\n",
    "        betas = []\n",
    "        \n",
    "    for i in tnrange(npretrain, desc=\"Pretrain\"):\n",
    "        sess.run(train_dual)\n",
    "\n",
    "    pbar = tnrange(niter+1, desc=\"Train\")\n",
    "    for i in pbar:\n",
    "        if i >= np.size(betas):\n",
    "            beta_i = 1.\n",
    "        else:\n",
    "            beta_i = betas[i]\n",
    "                           \n",
    "        _, lp, ld, td = sess.run(\n",
    "                [train_primal, loss_primal, loss_dual, mean_Td],\n",
    "                feed_dict={beta: beta_i}\n",
    "        )\n",
    "        \n",
    "        sess.run(train_dual)\n",
    "        sess.run(train_dual)\n",
    "            \n",
    "        pbar.set_description(\"lp=%.3f, ld=%.3f, td=%.3f\"  % (lp, ld, td))\n",
    "\n",
    "def get_samples(sess, nbatches=100):\n",
    "    zs = np.zeros([nbatches, batch_size, param_dim])\n",
    "    for i in range(nbatches):\n",
    "        zs[i] = sess.run(z_)\n",
    "    zs = zs.reshape(-1, param_dim)\n",
    "    return zs\n",
    "\n",
    "def stan_vb(stan_vb_alg=\"fullrank\", niter=10000):\n",
    "    stan_vb_out = \"./vb.out\"\n",
    "    sm.vb(data=data, sample_file=stan_vb_out, algorithm=stan_vb_alg, iter=niter, output_samples=10000, seed=1)\n",
    "    stan_vb_samples = np.genfromtxt(stan_vb_out, dtype=float, delimiter=',')\n",
    "    stan_vb_samples = stan_vb_samples[1:, 1:param_dim+1]\n",
    "\n",
    "    return stan_vb_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Close existing session if available\n",
    "try:\n",
    "    sess.close()\n",
    "except NameError:\n",
    "    pass\n",
    "sess = tf.InteractiveSession()\n",
    "sess.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Some parameters for the model fitting\n",
    "iter_max = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Run HMC\n",
    "stan_fit = sm.sampling(data=data, iter=500000, thin=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# AVB\n",
    "run_training(sess, data, niter=iter_max, npretrain=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:Automatic Differentiation Variational Inference (ADVI) is an EXPERIMENTAL ALGORITHM.\n",
      "WARNING:pystan:ADVI samples may be found on the filesystem in the file `./vb.out`\n",
      "WARNING:pystan:Automatic Differentiation Variational Inference (ADVI) is an EXPERIMENTAL ALGORITHM.\n",
      "WARNING:pystan:ADVI samples may be found on the filesystem in the file `./vb.out`\n"
     ]
    }
   ],
   "source": [
    "# Multiple VB\n",
    "stan_vb_samples_mf = stan_vb(\"meanfield\", iter_max)\n",
    "stan_vb_samples = stan_vb(\"fullrank\", iter_max)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parameters for visualization\n",
    "idx0, idx1 = 0, 1\n",
    "labels = [r'$\\mu$', r'$\\tau$', r'$\\eta_1$']\n",
    "xlabel = labels[idx0]\n",
    "ylabel = labels[idx1]\n",
    "\n",
    "plt.rc('font', size=16)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STAN HMC\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qIMM//941vn9VlVeyKZ3/dGGTsUKaEEibGvWuh+UFZAyNEAlSEHghIRIZCjqu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nJRwqEYN+dkQqkzHcV1Zd3qXLXBeLFGRzpCVyay4gXRm4vRm4txcaLElQUtdJoQDLUm2NOdYk9X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ca096b4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ca0e720f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d04060710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1fP+VJJuBa4HjgFt7tj1QVevn2lGSI4HTgbOq6pru2FpgBvggsGqEfavLax8kzcfIAqQv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\n/wAUwnTbRtc2fQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ca10aecf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def expand_vec(a):\n",
    "    if a.ndim == 1:\n",
    "        return a.reshape(-1, 1)\n",
    "    else:\n",
    "        return a\n",
    "    \n",
    "stan_res = stan_fit.extract()\n",
    "q = np.concatenate([expand_vec(l) for l in stan_res.values()], axis=1)\n",
    "\n",
    "q1 = q[:, idx0]\n",
    "q2 = q[:, idx1]\n",
    "\n",
    "q1_mean = q1.mean()\n",
    "q1_std = q1.std()\n",
    "\n",
    "q2_mean = q2.mean()\n",
    "q2_std = q2.std()\n",
    "\n",
    "bbox = [q1_mean - 4*q1_std, q1_mean + 4*q1_std,\n",
    "        q2_mean - 4*q2_std, q2_mean + 4*q2_std]\n",
    "scatter(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "kde(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "hist(q1)\n",
    "hist(q2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AVB\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mmRnK0ei52F6w6xa8XxuQUnJtvcPNao+0oZEzdUaLab729DTZ1NbXHRkt8MrV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ri2qbL8rZbT1HvEEVWX11LOzxSZyltUvPfNZK5K05Fs744xkF4fAbub2HRiemAwxbszxSVZxi1e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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d557a2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ca0927710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d57982860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6V92uqjrUp+4UOpetJEkjMsxgWE5nDKLX/uZ52YB1y4fYJknSJM2b21WTbEiyM8nOvXv3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ca0a68908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = get_samples(sess, nbatches=20)\n",
    "\n",
    "q1 = q[:, idx0]\n",
    "q2 = q[:, idx1]\n",
    "\n",
    "q1_mean = q1.mean()\n",
    "q1_std = q1.std()\n",
    "\n",
    "q2_mean = q2.mean()\n",
    "q2_std = q2.std()\n",
    "\n",
    "bbox = [q1_mean - 4*q1_std, q1_mean + 4*q1_std,\n",
    "        q2_mean - 4*q2_std, q2_mean + 4*q2_std]\n",
    "\n",
    "scatter(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "kde(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "hist(q1)\n",
    "hist(q2)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## STAN VB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6h60dm7wmZZmk8mbv+GIviGY6178if/PMIq/PXB14Pz5Tw1SKjxwa4boqzfrq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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d5c297780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d5c2977b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lwPHAJuC+hdKhe3B8AP4e+IOm13/2vLHDcwDwCapbxb/fYd0F3X/o7tjAwu87FwHvAJcC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\nfIoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d5c697c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d530f0cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = stan_vb_samples\n",
    "q1 = stan_vb_samples[:, idx0]\n",
    "q2 = stan_vb_samples[:, idx1]\n",
    "\n",
    "\n",
    "scatter(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "kde(q1, q2, bbox, xlabel=xlabel, ylabel=ylabel)\n",
    "hist(q1)\n",
    "hist(q2)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "widgets": {
   "state": {
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    "e14471633b9b46899eb834e040774d6d": {
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   },
   "version": "1.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
